5,135 research outputs found
Remarks on topological models and fractional statistics
One of the most intriguing aspects of Chern-Simons-type topological models is the fractional statistics of point particles which has been shown essential for our understanding of the fractional quantum Hall effects. Furthermore these ideas are applied to the study of high Tc superconductivity. We present here an recently proposed model for fractional spin with the Pauli term. On the other hand, in D=4 space-time, a Schwarz-type topological gauge theory with antisymmetric tensor gauge field, namely BF model, is reviewed. Antisymmetric tensor fields are conjectured as mediator of string interaction. A dimensional reduction of the previous model provides a (2+1) dimensional topological theory, which involves a 2-form B and a 0-form . Some recent results on this model are reported. Recently, there have been thoughts of generalizing unusual statistics to extended objects in others space-time dimensions, and in particular to the case of strings in four dimensions. In this context, discussions about fractional spin and antisymmetric tensor field are presented
Three-dimensional fractional-spin gravity
Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern--Simons
models consisting of fractional-spin fields coupled to higher-spin gravity and
internal non-abelian gauge fields. The gauge algebras consist of
Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal
algebras intertwined by infinite-dimensional generators in lowest-weight
representations of the Lorentz algebra with fractional spin. In integer or
half-integer non-unitary cases, there exist truncations to gl(N,N +/- 1) or
gl(N|N +/- 1) models. In all non-unitary cases, the internal gauge fields can
be set to zero. At the semi-classical level, the fractional-spin fields are
either Grassmann even or odd. The action requires the enveloping-algebra
representation of the deformed oscillators, while their Fock-space
representation suffices on-shell.Comment: 38 pages, 2 tables. References [7,13,61] added with comments in the
second version. To appear in JHE
A note on the topological order of noncommutative Hall fluids
We evaluate the ground state degeneracy of noncommutative Chern-Simons models
on the two-torus, a quantity that is interpreted as the "topological order" of
associated phases of Hall fluids. We define the noncommutative theory via
T-duality from an ordinary Chern-Simons model with non-abelian 't Hooft
magnetic fluxes. Motivated by this T-duality, we propose a discrete family of
noncommutative, non-abelian fluid models, arising as a natural generalization
of the standard noncommutative Chern-Simons effective models. We compute the
topological order for these universality classes, and comment on their possible
microscopic interpretation.Comment: 14 page
Particle Physics and Condensed Matter: The Saga Continues
Ideas from quantum field theory and topology have proved remarkably fertile
in suggesting new phenomena in the quantum physics of condensed matter. Here
I'll supply some broad, unifying context, both conceptual and historical, for
the abundance of results reported at the Nobel Symposium on "New Forms of
Matter, Topological Insulators and Superconductors". Since they distill some
most basic ideas in their simplest forms, these concluding remarks might also
serve, for non-specialists, as an introduction.Comment: 18 pages, 3 figures. Invited presentation of concluding remarks at
Nobel Symposium 156 on New Forms of Matter, Topological Insulators and
Superconductors, June 13-15 2014, H\"ogberga G{\aa}rd, Stockhol
Remarks on Charged Vortices in the Maxwell-Chern-Simons Model
We study vortex-like configuration in Maxwell-Chern-Simons Electrodynamics.
Attention is paid to the similarity it shares with the Nielsen-Olesen solutions
at large distances. A magnetic symmetry between a point-like and an
azimuthal-like current in this framework is also pointed out. Furthermore, we
address the issue of a neutral and spinless particle interacting with a charged
vortex, and obtain that the Aharonov-Casher-type phase depends upon mass and
distance parameters.Comment: New refs. added. Version accepted for publication in Phys. Lett.
Topological and symmetry broken phases of Z_N parafermions in one dimension
We classify the gapped phases of Z_N parafermions in one dimension and
construct a representative of each phase. Even in the absence of additional
symmetries besides parafermionic parity, parafermions may be realized in a
variety of phases, one for each divisor n of N. The phases can be characterized
by spontaneous symmetry breaking, topology, or a mixture of the two. Purely
topological phases arise if n is a unitary divisor, i.e. if n and N/n are
co-prime. Our analysis is based on the explicit realization of all symmetry
broken gapped phases in the dual Z_N-invariant quantum spin chains.Comment: 16 pages; v2: improved exposition and additional reference
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